Prove that if X and Y are independent standard normal random variables, then X + Y and X Y are independent random variables. This is a special case of the following important theorem. Let X and Y be independent random variables with a common distribution F. The random variables X + Y and X Y are independent if and only if F is a normal distribution function.

Thursday, January 5 th Kim Gilbert Kimgilb@uga.edu TA Office Hours, Boyd Room 204 • Monday 11:15 am – 5:30 pm • Friday 11:15 am – 3:30 pm Case Study: Helper vs. Hinderer • If infants have no preference, then the outcome...